This is really cool, but there's real-world instrument physics that might not be captured by simple Fourier transform templates, like a trumpet playing softly can have a significantly different harmonic spectrum than the same trumpet playing loudly, even at the same pitch

Trumpets produce a rich harmonic series with strong overtones, meaning their Fourier transform would show prominent peaks at integer multiples of the fundamental frequency. Instruments like flutes have more pure tones, but brass instruments typically have stronger higher harmonics, which would lead to more complex partial derivatives in the matrix equation shown in the article

So this script uses bandpass filtering and cross-correlation of attack/release envelopes to identify note timing. Given that brass instruments can exhibit non-linear behavior where the harmonic content changes significantly with playing intensity (think of the brightness difference between pp and ff passages), not sure how would this algorithm could handle intensity-dependent timbral variations. I'd consider adding intensity-dependent Fourier templates for each instrument to improve accuracy